Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 41, 15 pp.
Asymptotics of the rising moments for the coupon collector's problem
We develop techniques of computing the asymptotics of the moments of the number $T_N$ of coupons that a collector has to buy in order to find all $N$ existing different coupons as $N\rightarrow \infty.$ The probabilities (occurring frequencies) of the coupons can be quite arbitrary. After mentioning the case where the coupon probabilities are equal we consider the general case (of unequal probabilities). For a large class of distributions (after adopting a dichotomy) we arrive at the leading behavior of the moments of $T_N$ as $N\rightarrow \infty.$ We also present various illustrative examples.
Electron. J. Probab., Volume 18 (2013), paper no. 41, 15 pp.
Accepted: 22 March 2013
First available in Project Euclid: 4 June 2016
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Doumas, Aristides; Papanicolaou, Vassilis. Asymptotics of the rising moments for the coupon collector's problem. Electron. J. Probab. 18 (2013), paper no. 41, 15 pp. doi:10.1214/EJP.v18-1746. https://projecteuclid.org/euclid.ejp/1465064266